Conservation laws and Lie symmetries a (2+1)-dimensional thin film equation

  • Elena RecioEmail author
  • Tamara M. Garrido
  • Rafael de la Rosa
  • María S. Bruzón
Original Paper


This paper considers a generalized thin film equation in two spatial dimensions depending on three arbitrary functions. This equation describes the time evolution of a Newtonian liquid that is considerably thinner in one direction than in the other directions. We include a classification of point symmetries and the corresponding transformation groups. We derive all low-order local conservation laws of the equation in terms of the arbitrary functions. In addition, we discuss the physical meaning of the conserved quantities and provide a useful conservation identity.


Thin film equation Lie symmetries Conservation laws Conservation identity 



The authors gratefully acknowledge Dr. Stephen Anco from Brock University for his expert guidance and help during his visit to Universidad de Cádiz. The authors express their sincerest gratitude to the Plan Propio de Investigación de la Universidad de Cádiz.


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Departamento de MatemáticasUniversidad de CádizCádizSpain

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